Given rational number is 64/455
p/q is terminating if
a) p and q are co-prime &
b) q is of the form of 2n 5m where n and m are non-negative integers.
Firstly, we check co-prime
64 = 26
455 = 5 × 7 × 13
64 and 455 have no common factors
Therefore, 64 and 455 are co-prime.
Now, we have to check that q is in the form of 2n5m
455 = 5 × 7 × 13
So, denominator is not of the form 2n5m
Thus, 64455 is a non-terminating repeating decimal.